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Commutability of Gamma-Limits in Problems with Multiple Scales.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin :
Logos Verlag Berlin,
2017.
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| Colección: | Augsburger Schriften Zur Mathematik, Physik und Informatik Ser.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Intro; 1 Motivation from elasticity; 1.1 Variational formulation; 1.2 Linear elasticity; 1.3 Geometric linearization in the multiwell case; 1.4 Homogenization; 1.5 Commutability of geometric linearization and homogenization; 2 The p> 1 case; 2.1 Concept of Î#x93;-closure; 2.2 Î#x93;-closure under standard growth assumptions; 2.3 Î#x93;-closure for GÃÆrding type functionals; 2.4 Boundary values and compactness; 2.5 A perturbation and a relaxation result; 2.6 Commutability of Î#x93;-limits; 2.7 Homogenization of GÃÆrding type functionals; 3 Applications in elasticity theory.
- 3.1 Functionals for microstructured multiwell materials3.2 Homogenization and geometric linearization; 3.3 Additional comments; 4 Stochastic homogenization; 4.1 Ergodic theory; 4.2 Stochastic homogenization; 5 The p = 1 case; 5.1 Counterexample; 5.2 Î#x93;-closure; 6 Hencky plasticity setting; 6.1 Hencky plasticity; 6.2 One-dimensional toy model; 6.2.1 Convex homogenization; 6.2.2 Zero hardening; 6.2.3 Small hardening; 6.2.4 Commutability of homogenization and vanishing hardening; 6.3 Setting the problem; 7 Functions of bounded deformation; 7.1 Functions of bounded deformation.
- 7.1.1 Definition and basic properties7.1.2 Albertiâ#x80;#x99;s rank one theorem; 7.1.3 Approximate differentiability; 7.1.4 Kernel of Edev; 7.2 Space U; 7.2.1 Definition and basic properties; 7.2.2 Helmholtz decomposition; 7.3 Bogovskiiâ#x80;#x99;s operator; 8 Commutability of homogenization and vanishing hardening; 8.1 Setting; 8.2 Homogenized density; 8.3 (
- )-strict continuity of G; 8.4 lim inf-inequality at zero hardening; 8.4.1 Regular points; 8.4.2 Singular points; 8.5 Conclusion; 8.6 Relaxation at zero hardening revisited.